We use as a classical light source a single-mode thermal state with mean photon number \(\bar{n}_{\textrm {S}}\)  given by[1]},
\(\hat{\rho }_{\textrm {th}}=\sum _{n=0}^\infty \frac{\bar{n}_{\textrm {S}}^n}{(1+\bar{n}_{\textrm {S}})^{n+1}}{\vert n \rangle }{\langle n \vert },\) 
